Message #3821

From: Eduard Baumann <>
Subject: Melinda’s physical 2^4 puzzle, mirrors
Date: Sat, 18 Nov 2017 10:59:12 +0100


Making (manufacturing) a physical 2^4 puzzle you have to chose the right mirrored 4-color cubicle of two possible ones for each of the 16 (8 over 4) color combinations which don’t contain any opponent color pair. You can also manufacture the mirrored physical 2^4 puzzle. Now these two physical 2^4 cannot be transformed on in the other with 3D operations. On the other side a 3D view (projection) of the virtual 2^4 can be transformed in his mirror ! See

Is something wrong in this consideration?
If yes, what?

Please read carefully my message.

Best regards

—– Original Message —–
From: Marc Ringuette [4D_Cubing]
Sent: Friday, November 17, 2017 8:38 PM
Subject: Re: [MC4D] Melinda’s physical 2^4 puzzle, full puzzle rotations

On 11/16/2017 2:22 PM, ‘Eduard Baumann’ [4D_Cubing] wrote:

BIG question. Is it possible to change the two "inverted" colors by simple moves?

Hi, Ed,

I think you’re asking about what Melinda calls a full-puzzle rotation. Yes, this is key to being able to solve the full 2^4 puzzle in the same way on both the virtual and the physical versions. You can use either of these two move sequences to do it.

Melinda’s new video of her classic FOro:
Marc’s alternative FOro using the ROIL moveset:

I call the result of these sequences FOro, because they both correspond to the single click MC4D move that is a Front-Out ROtation.

Here’s an old video of mine, cued up to 2:30 where I demonstrate Melinda’s classic FOro while I carefully keep the puzzle oriented on a desk. At the end I show the MC4D equivalent of the rotation I just did (at about 3:25 of the video).

I wonder who is going to be the first person to solve the physical 2^4 puzzle? It’s not me, yet. I’ve been waiting for more people to have the puzzle before I get back to trying to solve it. I’ve come up with a 3-cycle algorithm, though, so that’s a good start. I also have a long solution to the "double twisted corner" problem, I think, but I really want to come to a more thorough understanding of the 12 orientations of the 4-color pieces of a 4D hypercube.

A good milestone will be when somebody generates an MC4D scramble, sets up that position on their physical puzzle, and then solves it on the physical puzzle while following along with MC4D, resulting in both puzzles being solved.


p.s. here’s a collection of my relevant videos of the physical 2^4 puzzle, so you don’t have to dig for them. I’ve omitted the ones that use the deprecated (parity violating) quarter puzzle moves. These are still marked "unlisted" in YouTube, at Melinda’s request, until her Public Release (TBD). These vids are not fantastic quality, but they’re what I’ve got.

2 over the shoulder intro v3
3 special rotations FUro and FOro
4 overlap of natural moves
07a a 3 cycle on phys 2^4
07b same 3 cycle on mc4d
12 ROIL moveset intro
13 ROIL version of FOro
14 ROIL scrambling
15 ROIL strict subset vs macro equivalents
16 ROIL meaning of junctions out positions